Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 442368 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4 |
| abelian | C2×C3×C4×C9×C16 |
| multiplicative | (ℤ/4199)ˣ, (ℤ/4403)ˣ, (ℤ/5661)ˣ, (ℤ/5967)ˣ, (ℤ/8398)ˣ, (ℤ/8806)ˣ, (ℤ/11322)ˣ, (ℤ/11934)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C8 | C23×C32 |
| socle, prime radical | C23×C32 | C2×C3×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1080 conjugacy classes of subgroups.
3456 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.